∫sec^3xdx 过程帮忙写下!谢谢。 ∫sec^3xdx的值
\u222bsec^3xdx=\uff1f\u222bsec³xdx
=\u222bsecxd(tanx)
=secxtanx-\u222btanxd(secx)
=secxtanx-\u222btan²xsecxdx
=secxtanx-\u222b(sec²x-1)secxdx
=secxtanx+\u222bsecxdx-\u222bsec³xdx
=secxtanx+ln|secx+tanx|-\u222bsec³xdx
\u6240\u4ee5\u222bsec³xdx=(secxtanx+ln|secx+tanx|\uff09/2+C
\u79ef\u5206\u662f\u5fae\u79ef\u5206\u5b66\u4e0e\u6570\u5b66\u5206\u6790\u91cc\u7684\u4e00\u4e2a\u6838\u5fc3\u6982\u5ff5\u3002\u901a\u5e38\u5206\u4e3a\u5b9a\u79ef\u5206\u548c\u4e0d\u5b9a\u79ef\u5206\u4e24\u79cd\u3002 [2] \u76f4\u89c2\u5730\u8bf4\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u5b9e\u51fd\u6570f\uff08x\uff09\uff0c\u5728\u533a\u95f4[a\uff0cb]\u4e0a\u7684\u5b9a\u79ef\u5206\u8bb0\u4e3a\uff1a
\u82e5f\uff08x\uff09\u5728[a,b]\u4e0a\u6052\u4e3a\u6b63\uff0c\u53ef\u4ee5\u5c06\u5b9a\u79ef\u5206\u7406\u89e3\u4e3a\u5728Oxy\u5750\u6807\u5e73\u9762\u4e0a\uff0c\u7531\u66f2\u7ebf\uff08x\uff0cf\uff08x\uff09\uff09\u3001\u76f4\u7ebfx=a\u3001x=b\u4ee5\u53cax\u8f74\u56f4\u6210\u7684\u9762\u79ef\u503c\uff08\u4e00\u79cd\u786e\u5b9a\u7684\u5b9e\u6570\u503c\uff09\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u8bbe\u6709\u95ed\u533a\u95f4[a,b]\uff0c\u90a3\u4e48[a,b]\u7684\u4e00\u4e2a\u5206\u5272\u662f\u6307\u5728\u6b64\u533a\u95f4\u4e2d\u53d6\u4e00\u4e2a\u6709\u9650\u7684\u70b9\u5217 \u3002\u6bcf\u4e2a\u95ed\u533a\u95f4 \u53eb\u505a\u4e00\u4e2a\u5b50\u533a\u95f4\u3002
\u5b9a\u4e49 \u4e3a\u8fd9\u4e9b\u5b50\u533a\u95f4\u957f\u5ea6\u7684\u6700\u5927\u503c\uff1a \uff0c\u5176\u4e2d \u3002\u800c\u95ed\u533a\u95f4[a,b]\u4e0a\u7684\u4e00\u4e2a\u53d6\u6837\u5206\u5272\u662f\u6307\u5728\u8fdb\u884c\u5206\u5272 \u540e\uff0c\u4e8e\u6bcf\u4e00\u4e2a\u5b50\u533a\u95f4\u4e2d \u53d6\u51fa\u4e00\u70b9 \u3002
\u5bf9\u4e00\u4e2a\u5728\u95ed\u533a\u95f4[a,b]\u6709\u5b9a\u4e49\u7684\u5b9e\u503c\u51fd\u6570f\uff0cf\u5173\u4e8e\u53d6\u6837\u5206\u5272
\u81f3\u4e8e\u4e00\u822c\u7684\uff08\u6709\u6b63\u6709\u8d1f\u7684\uff09\u53ef\u6d4b\u51fd\u6570f\uff0c\u5b83\u7684\u79ef\u5206\u662f\u51fd\u6570\u66f2\u7ebf\u5728x\u8f74\u4e0a\u65b9\u201c\u56f4\u51fa\u201d\u7684\u9762\u79ef\uff0c\u51cf\u53bb\u66f2\u7ebf\u5728x\u8f74\u4e0b\u65b9\u201c\u56f4\u51fa\u201d\u7684\u9762\u79ef\u3002\u4e25\u683c\u5b9a\u4e49\u9700\u8981\u5f15\u8fdb\u201c\u6b63\u90e8\u51fd\u6570\u201d\u548c\u201c\u8d1f\u90e8\u51fd\u6570\u201d\u7684\u6982\u5ff5\uff1a
\u5982\u679c \u5219 \u5426\u5219
\u5982\u679c \u5219 \u53ef\u4ee5\u9a8c\u8bc1\uff0c\u603b\u6709
\u800cf\u7684\u79ef\u5206\u5b9a\u4e49\u4e3a\uff1a \u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1---\u79ef\u5206
\u7b80\u5355\u8ba1\u7b97\u4e00\u4e0b\u5373\u53ef\uff0c\u7b54\u6848\u5982\u56fe\u6240\u793a
简单计算一下即可，答案如图所示
扩展阅读：∫x∧3e∧x∧2dx ... ∫ x a dx ... xsin 4xdx ... ∫e xsinxdx ... ∫sin 3xcosxdx ... x∧2e∧x ... ∫ 1-x dx ... fsinx 2dx ... ∫sec 2xdx ...
